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10-2. Parabola, Ellipse, Hyperbola
easy
The equation of the ellipse whose vertices are $( \pm 5,\;0)$ and foci are $( \pm 4,\;0)$ is
A
$9{x^2} + 25{y^2} = 225$
B
$25{x^2} + 9{y^2} = 225$
C
$3{x^2} + 4{y^2} = 192$
D
None of these
Solution
(a) Vertices $( \pm 5,\,0) \equiv ( \pm a,\,0)$ $⇒ a = 5$
Foci $( \pm 4,\,0) \equiv ( \pm ae,\,0)$
$e = \frac{4}{5}$,
$b = (5)\,\left( {\frac{3}{5}} \right) = 3$
Hence equation is $\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{9} = 1$
$i.e.$, $9{x^2} + 25{y^2} = 225$.
Standard 11
Mathematics